In 1988 Shafarevich asked me to write a volume for the Encyclopaedia of Mathematical Sciences on Diophantine Geometry. I said yes, and here is the volume. By definition, diophantine problems concern the solutions of equations in integers, or rational numbers, or various generalizations, such as finitely generated rings over Z or finitely generated fields over Q. The word Geometry is tacked on to suggest geometric methods. This means that the present volume is not elementary. For a survey of some basic problems with a much ...
Read More
In 1988 Shafarevich asked me to write a volume for the Encyclopaedia of Mathematical Sciences on Diophantine Geometry. I said yes, and here is the volume. By definition, diophantine problems concern the solutions of equations in integers, or rational numbers, or various generalizations, such as finitely generated rings over Z or finitely generated fields over Q. The word Geometry is tacked on to suggest geometric methods. This means that the present volume is not elementary. For a survey of some basic problems with a much more elementary approach, see [La 9Oc]. The field of diophantine geometry is now moving quite rapidly. Out standing conjectures ranging from decades back are being proved. I have tried to give the book some sort of coherence and permanence by em phasizing structural conjectures as much as results, so that one has a clear picture of the field. On the whole, I omit proofs, according to the boundary conditions of the encyclopedia. On some occasions I do give some ideasfor the proofs when these are especially important. In any case, a lengthy bibliography refers to papers and books where proofs may be found. I have also followed Shafarevich's suggestion to give examples, and I have especially chosen these examples which show how some classical problems do or do not get solved by contemporary in sights. Fermat's last theorem occupies an intermediate position. Al though it is not proved, it is not an isolated problem any more.
Read Less
Add this copy of Number Theory III: Diophantine Geometry (Encyclopedia to cart. $93.94, new condition, Sold by discount_scientific_books rated 5.0 out of 5 stars, ships from Sterling Heights, MI, UNITED STATES, published 1991 by Springer.
Add this copy of Number Theory III: Diophantine Geometry (Encyclopedia to cart. $94.48, new condition, Sold by discount_scientific_books rated 5.0 out of 5 stars, ships from Sterling Heights, MI, UNITED STATES, published 1991 by Springer.
Add this copy of Number Theory III: Diophantine Geometry to cart. $103.32, new condition, Sold by Ingram Customer Returns Center rated 5.0 out of 5 stars, ships from NV, USA, published 1997 by Springer-Verlag Berlin and Heidelberg GmbH & Co. K.
Edition:
1997, Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Add this copy of Number Theory III: Diophantine Geometry to cart. $103.32, new condition, Sold by Ingram Customer Returns Center rated 5.0 out of 5 stars, ships from NV, USA, published 1991 by Springer.
Add this copy of Number Theory III: Diophantine Geometry to cart. $113.51, new condition, Sold by GreatBookPrices rated 4.0 out of 5 stars, ships from Columbia, MD, UNITED STATES, published 1997 by Springer-Verlag Berlin and Heidelberg GmbH & Co. K.
Edition:
1997, Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Publisher:
Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Published:
1997
Language:
English
Alibris ID:
17988225915
Shipping Options:
Standard Shipping: $4.99
Choose your shipping method in Checkout. Costs may vary based on destination.
Seller's Description:
New. XIII, 296 p. Intended for college/higher education audience. In Stock. 100% Money Back Guarantee. Brand New, Perfect Condition, allow 4-14 business days for standard shipping. To Alaska, Hawaii, U.S. protectorate, P.O. box, and APO/FPO addresses allow 4-28 business days for Standard shipping. No expedited shipping. All orders placed with expedited shipping will be cancelled. Over 3, 000, 000 happy customers.
Add this copy of Number Theory III to cart. $114.59, new condition, Sold by Media Smart rated 3.0 out of 5 stars, ships from Hawthorne, CA, UNITED STATES, published 1997 by Springer.
Edition:
1997, Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Add this copy of Number Theory 3 to cart. $129.19, new condition, Sold by Media Smart rated 3.0 out of 5 stars, ships from Hawthorne, CA, UNITED STATES, published 1991 by Springer.
